Cluster algebras are commutative algebras with a special combinatorial structure. A cluster algebra is a subalgebra of a field of rational functions in several variables that is generated by a distinguished set of generators called cluster variables. These cluster variables are constructed recursively from an initial seed by a process called mutation. The algebra depends on the choice of an initial quiver (=oriented graph) which governs the mutation process. Cluster algebras are related to a number of research areas including representation theory of algebras and Lie algebras, combinatorics, algebraic and hyperbolic geometry, dynamical systems, and string theory. In this talk, we will present our recent work with Véronique Bazier-Matte establishing a connection between cluster algebras and knot theory. To every knot (or link) diagram, we associate a cluster algebra in which we identify a cluster whose cluster variables realize the Alexander polynomial of the knot. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.